There are hundreds of named Rhododendrons.
Azaleas actually come under the name Rhododendron.
Even experts with the shrub in front of them can struggle to accurately name them.
From pics it is almost impossible.
There are several glorious purple ones that it might be.
It is normal for some to flower in the spring and later on in late summer.
So this is just a suggestion.....it may not be correct.
Rhododendron impeditum...dwarf very slow growing, purple flowers.
Ours is in flower right now.
I am assuming the specimen in your pic is quite old.
